The earth orbits the sun at an approximate velocity v = 30 km/s and radius r = 150*10^6 km. (a) Assuming a circular orbit for the earth, what is the approximate mass of the sun? (b) If the mass of the sun was doubled, what would the new length of a year be? Assume the Earth remains in circular orbit about the sun at its usual orbital radius. Answer in terms of current years. (Hint: you do not need to plug in the value of G.)
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- The International Space Station is in a 210-mile-high orbit. What is the station's orbital speed? The radius of Earth is 6.37×10^6 m, its mass is 5.98×10^24kg. Express your answer with the appropriate units. What is the station's orbital period? Express your answer in minutes.Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun).Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. Part A Find the gravitational force of one star on the other. Express your answer in terms of G, M, R. Πν ΑΣφ ? F = Part B Find the orbital speed of each star. Express your answer in terms of G, M, R. να ΑΣΦ7 ? Part C
- When the Moon is directly overhead at sunset, the force by Earth on the Moon, FEM, is essentially at 90° to the force by the Sun on the Moon, FSM, as shown below. FEM=1.98×10^20N and FSM=4.36×10^20N, all other forces on the Moon are negligible, and the mass of the Moon is 7.35×10^22kg. 1. Write an expression for the magnitude of the acceleration of the Moon. 2. What is the acceleration of the Moon in m/s^2?) One of the moors of Jupiter, named an orbital radius of 10 4.22 * 10 ^ 8 a period of 1.77 days. Assuming the orbitis circular, calculate the inass of Jupiter. (b) largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 * 10 ^ 9 m a period of 7.16 daysCalculate the mass of Jupiter from this data ) your results to parts (b) consistent ? Yes No ExplainAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.7 x 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be? yr (b) If its period is 5.2 x 10 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar masses
- Suppose an object is traveling in a circle of radius 10 m. if the object has a period of 6 s, what is its orbital speed (in m/s)?Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v| = 225 km/s and the orbital period of each is 11.6 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) M XCM M Part 1 of 3 - Conceptualize From the given data, it is difficult to estimate a reasonable answer to this problem without working through the details and actually solving it. A reasonable guess might be that each star has a mass equal to or slightly larger than our Sun because fourteen days is short compared to the periods of all the Sun's planets. Part 2 of 3 - Categorize The only force acting on each star is the central gravitational force of attraction which results in a centripetal acceleration. When we solve Newton's second law, we can find the unknown mass in terms of the variables…A sun rays take about 8 minutes to reach the Earth surface travelling at constant speed v= 3,0 * 10^8 m/s. How far is earth from the sun?
- According to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is approximately 3.82 x 105 km. The Moon orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month). Calculate the orbital velocity of the Moon in m/s.Consider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 10¹¹ solar masses. A star orbiting near the galaxy's periphery is 5.9 x 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) What should the orbital period of that star be? yr If its period is 5.8 x 107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar masses